Paul Bittar, the chief executive of the British Horseracing Authority, said on Sunday that racing should not rush into fresh changes to the Grand National in the aftermath of Saturday's race, in which two horses, including Synchronised, the Gold Cup winner, suffered fatal injuries.

A number of amendments were made to the course following the 2011 National, in which two horses also died, including a two-inch reduction in the height of the fourth (and 20th) fence and a reduction in the drop on the landing side of Becher's Brook by between four and five inches, while all runners were required to have finished at least fourth in a steeplechase. The landing side of the first (and 17th) was also levelled out.

Bittar said that it would take time to assess the impact of the changes, and that it would be "premature to suggest that modifications to the course and other changes have not been effective or will not yet prove to be effective".

Extending his "deepest sympathies" to the connections of Synchronised and According To Pete, who suffered a fatal injury when brought down at Becher's Brook on the second circuit, Bittar said that the authority is "reasonably advanced in the process of examining the incidents" which led to the deaths of the two horses.

He added: "In November last year, the BHA published the findings from a comprehensive and detailed review of all elements of the Grand National.

"Since the review and the implementation of changes, four races have been held over the course without incident prior to yesterday's running of the Grand National.

"The evidence indicates that the changes and improvements in safety made over the years have led to an overall decrease in injury and fatalities, both on the Grand National course and racing in general. Naturally our objective is for there to be no fatalities, but we also recognise that we cannot remove risk altogether from such a competitive activity."

The continued use of "drop" fences at Aintree was highlighted by David Muir, an equine consultant with the RSPCA. Julian Thick, the managing director of Aintree, said on Sunday that it was "much too early" to say whether any significant changes will be made to Becher's Brook, the most famous obstacle on the course.

"We will look seriously at all aspects of the race, but it is far too early to come to any conclusions," Thick said. "We will never stand still on safety, but risk is an inherent part of many sports."

Paul Nicholls, whose narrow victory in Saturday's race with the now-retired Neptune Collonges guaranteed him a seventh win in the trainers' championship, said on Sunday that it was regrettable that the deaths of Synchronised and According To Pete had diverted attention from the winner's performance.

"It's a shame the headlines are not about what was a wonderful race," Nicholls said. "Of course it was a tragedy [that two horses died] and there are lessons to be learned, but you've got to reflect on the winner as well.

"Look at how many people were at Aintree enjoying it. Whether they do anything about the fences or the number of runners, I know the race is in good hands. But you can never make it a risk-free sport."

Frank Berry, the racing manager to JP McManus, the owner of Synchronised, said that the horse's death was "just one of those things" and added: "The horse looked perfect when he got up from the fall and he galloped away and jumped away afterwards. When he was up and running again, you'd be hoping he'd be fine afterwards, they usually are, but what happened, happened and it was very sad.

"It's a sad day, particularly for everyone in Jackdaws' [Castle, the yard of Jonjo O'Neill, Synchronised's trainer]. He was always a popular horse in the yard, even before he won the Gold Cup."